exteriorPower(ZZ,AbstractSheaf)

Synopsis

• Function: exteriorPower

• Usage:

  exteriorPower(n,F)

  exteriorPower_n F

• Inputs:
  • n, an integer
  • F, an abstract sheaf
• Optional inputs:
  • Strategy => ..., default value null,
• Outputs:
  • an abstract sheaf, the $n$-th exterior power of $F$

Description

i1 : tangentBundle abstractProjectiveSpace 4

o1 = a sheaf

o1 : an abstract sheaf of rank 4 on a flag bundle

i2 : exteriorPower_4 oo

o2 = a sheaf

o2 : an abstract sheaf of rank 1 on a flag bundle

i3 : chern oo

o3 = 1 + 5H
           2,1

                                QQ[][h, H   ..H   ]
                                         2,1   2,4
o3 : ------------------------------------------------------------------------
     (- h - H   , - h*H    - H   , - h*H    - H   , - h*H    - H   , -h*H   )
             2,1       2,1    2,2       2,2    2,3       2,3    2,4      2,4

See also

• symmetricPower(RingElement,AbstractSheaf) -- symmetric power of an abstract sheaf
• schur(List,AbstractSheaf) -- apply a Schur functor to an abstract sheaf
• determinant(AbstractSheaf) -- determinant of an abstract sheaf